I suspect your custom installer could be made a little smarter. There are plenty of APIs (such as MsiQueryProductState) that will tell you if that exact ProductCode is installed, and ways to get the version (MsiGetProductInfo). My guess is that your custom installer is just firing off all the MSI installs without checking if they are already installed, hence the Remove prompts.
Your general plan should be to have some data available to your custom installer that it can use to find out what's already installed and what the versions are, and then compare these with what you are about to install. Use those APIs. If the product is already installed then skip the install. If you have a newer version (that you built with the WiX MajorUpgrade element) then just install it because it will replace the existing older one.
There's nothing I can think of in WiX that would automatically reinstall a product that your custom installer caused removal of by re-installing it and prompting the user to remove it, if that's what's going on.